This paper examines in a new way some known facts about numerical semigroups especially when the number of minimal generators (that is the embedding dimension) is at most three and at least two minimal generators are coprime; for such semigroups an algorithm is reinvestigated to find the pseudo-Frobenius numbers, in particular we fully characterize those of $\langle a,a+1,a+p\rangle$ for any $p\ge 2$, $\langle ab+a+1,bc+b+1,ca+c+1\rangle$ and consider $\langle n^2,(n+1)^2,(n+2)^2\rangle$ semigroups; a particular family of $n$ dimensional numerical semigroups of type at most $n-1$ is also given.